Computation of Length of Operating Cycle:

Operating Cycle = Day's Sales of Inventory + Day's Sales Outstanding

Here,

Day's Sales of Inventory = 360/Cost of Goods Sold*Average Inventories = 360/66*((10+16)/2) = 360/66*13 = 70.91 days 

Day's Sales Outstanding = 360/Sales*Average Accounts Receivables = 360/90*((14+20)/2) = 360/90*17 = 68 days 

Operating Cycle = 70.91 days + 68 days = 138.91 days

Computation of Cash Operating Cycle:

 Cash Operating Cycle = Day's Sales of Inventory + Day's Sales Outstanding - Day's Payable Outstanding

Here,

Day's Payable Outstanding =  360/Cost of Goods Sold*Average Accounts Payable = 360/66*((10+16)/2) = 360/66*13 = 70.91 days 

Cash Operating Cycle = 70.91 days + 68 days - 70.91 days = 68 days